Class 12

Math

Algebra

Probability I

A card is drawn at random from a pack of cards. What ist the probability that the drawn card is neither a heart nor a king?

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Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

An electrical system has open-closed switches $S_{1},S_{2}andS_{3}$ as shown in fig. The switches operate independently of one another and the current will flow from $A→B$ either if $S_{1}$ is closed or if both $S_{2}andS_{3}$ are closed. If $P(S_{1})=P(S_{2})=P(S_{3})=1/2,$ then find the probability that the circuit will work. fig

Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).

A coin is tossed three times, consider the following events.A : ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘Atleast two appear’.Do they form a set of mutually exclusive and exhaustive events?

A coin is tossed twice, what is the probability that atleast one tail occurs?

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

An urn contains 6 white and 4 black balls. A fair die is rolled and that number of balls we chosen from the urn. Find the probability that the balls selected are white.

Describe the sample space for the indicated experiment : One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.